Spectral projectors, resolvent, and Fourier restriction on the hyperbolic space

We develop a unified approach to proving Lp-Lq boundedness of spectral projectors, the resolvent of the Laplace-Beltrami operator and its derivative on IH[d. In the case of spectral projectors, and when p and q are in duality, the dependence of the implicit constant on p is shown to be sharp. We also give partial results on the question of Lp - Lq boundedness of the Fourier extension operator. As an application, we prove smoothing estimates for the free Schrodinger equation on IH[d and a limiting absorption principle for the electromagnetic Schrodinger equation with small potentials.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

We propose a unified approach to prove the Lp-Lq boundedness of spectral projectors, the resolvent of the Laplace-Beltrami operator, and its derivative on IH[d. The dependence of the implicit constant on p is shown to be sharp when p and q are in duality for spectral projectors. Partial results on the Lp-Lq boundedness of the Fourier extension operator are also provided. As applications, we prove smoothing estimates for the free Schrödinger equation on IH[d and a limiting absorption principle for the electromagnetic Schrödinger equation with small potentials.